修改 Spirograph 代码以获得更多控制

Question

dx在旧版图片中添加一些功能（如域和）非常容易spiro。我只关注您的两个屏幕截图以进行说明，但我认为您可以使用调整后的语法完成所有这些操作。如果我遗漏了什么，请告诉我。

\documentclass[tikz,border=3mm]{standalone}
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples}] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.005,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzpicture}[]
 \draw 
   (0,0) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {pic[scale=0.5,draw=\X,ultra
   thick]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}};
 \draw(0,-7) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {foreach \Z in {0,...,5}
   {pic[scale=0.5,draw=\X,ultra thick,fill=\X,fill
   opacity=0.2,rotate=\Z*15]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}}};  
\end{tikzpicture}
\end{document}

请注意，旧版本使用了，smooth cycle因此可以用相对较少的样本获得良好的结果。另一方面，在这里，我按照您的指示用直线连接绘图点，因此需要更多样本和更长的编译时间。请告诉我是否应该返回该smooth案例以提高速度。这样做会产生

\documentclass[tikz,border=3mm]{standalone}
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples},smooth] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.05,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzpicture}
 \draw 
   (0,0) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {pic[scale=0.5,draw=\X,ultra
   thick]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}};
 \draw(0,-7) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {foreach \Z in {0,...,5}
   {pic[scale=0.5,draw=\X,ultra thick,fill=\X,fill
   opacity=0.2,rotate=\Z*15]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}}};  
\end{tikzpicture}
\end{document}

对我来说，将其与路径衰落结合起来似乎很自然。

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{shadings,fadings}
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples},smooth] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.05,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzfadingfrompicture}[name=spiro]
\draw foreach \Y in {0,...,3}
   {foreach \Z in {0,...,5}
   {pic[scale=0.5,fill=transparent!60,
   draw=transparent!20,
   rotate=\Z*15]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/2+pi/9+\Y*pi/2}}}}};  
\end{tikzfadingfrompicture}
\begin{tikzpicture}
 \shade[shading=color wheel,
  path fading=spiro,fit fading=false] (0,0) circle [radius=4cm];
\end{tikzpicture}
\end{document}

附录：这些是要求的图表。我在代码中添加了一些解释。要很好地解释某件事，需要了解其他用户遇到的困难。我没有这方面的知识。如果你问具体的问题，我会尽力回答。

\documentclass[tikz,border=3mm]{standalone}
% The following just sets up a plot where you can contol the parameters via pgf
% keys. The central object is the plot.
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples},smooth] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.08,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzpicture}
 \path (0,0)  
  pic[scale=0.5,draw=yellow,ultra   thick]{spiro2={dx=0.03}}
   foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {pic[scale=0.5,draw=\X,ultra
   thick]{spiro2={domain={-pi/12+\Y*pi/2}:{pi/12+\Y*pi/2}}}};
 % This is a loop orgy. We loop over scale factors, overall rotations and colors.   
 \path[line cap=round] (7,0)  
   foreach \ScaleN 
    [evaluate=\ScaleN as \Scale using {pow(0.85,\ScaleN)/0.8}] % compute sale factor
    in {1,...,5} %loop over scale
     {foreach \Z in {0,...,3} %loop over 4 overall rotations
       {foreach \X [count=\Y starting from 0] in 
         {yellow,orange,red,blue,purple,cyan,magenta,green!70!black} % colors
       {pic[scale=0.5,draw=\X,rotate=\Y*90/8+\Z*90,
       scale=\Scale,line width=\Scale*2pt]
       {spiro2={domain={-pi/11.4}:{pi/11.4}}}}}};
\end{tikzpicture}
\end{document}

Answer 1

dx在旧版图片中添加一些功能（如域和）非常容易spiro。我只关注您的两个屏幕截图以进行说明，但我认为您可以使用调整后的语法完成所有这些操作。如果我遗漏了什么，请告诉我。

\documentclass[tikz,border=3mm]{standalone}
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples}] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.005,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzpicture}[]
 \draw 
   (0,0) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {pic[scale=0.5,draw=\X,ultra
   thick]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}};
 \draw(0,-7) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {foreach \Z in {0,...,5}
   {pic[scale=0.5,draw=\X,ultra thick,fill=\X,fill
   opacity=0.2,rotate=\Z*15]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}}};  
\end{tikzpicture}
\end{document}

请注意，旧版本使用了，smooth cycle因此可以用相对较少的样本获得良好的结果。另一方面，在这里，我按照您的指示用直线连接绘图点，因此需要更多样本和更长的编译时间。请告诉我是否应该返回该smooth案例以提高速度。这样做会产生

\documentclass[tikz,border=3mm]{standalone}
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples},smooth] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.05,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzpicture}
 \draw 
   (0,0) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {pic[scale=0.5,draw=\X,ultra
   thick]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}};
 \draw(0,-7) foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {foreach \Z in {0,...,5}
   {pic[scale=0.5,draw=\X,ultra thick,fill=\X,fill
   opacity=0.2,rotate=\Z*15]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/4+\Y*pi/2}}}}};  
\end{tikzpicture}
\end{document}

对我来说，将其与路径衰落结合起来似乎很自然。

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{shadings,fadings}
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples},smooth] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.05,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzfadingfrompicture}[name=spiro]
\draw foreach \Y in {0,...,3}
   {foreach \Z in {0,...,5}
   {pic[scale=0.5,fill=transparent!60,
   draw=transparent!20,
   rotate=\Z*15]{spiro2={domain={-pi/4+(\Y-1)*pi/2}:{-pi/2+pi/9+\Y*pi/2}}}}};  
\end{tikzfadingfrompicture}
\begin{tikzpicture}
 \shade[shading=color wheel,
  path fading=spiro,fit fading=false] (0,0) circle [radius=4cm];
\end{tikzpicture}
\end{document}

附录：这些是要求的图表。我在代码中添加了一些解释。要很好地解释某件事，需要了解其他用户遇到的困难。我没有这方面的知识。如果你问具体的问题，我会尽力回答。

\documentclass[tikz,border=3mm]{standalone}
% The following just sets up a plot where you can contol the parameters via pgf
% keys. The central object is the plot.
\tikzset{pics/spiro2/.style={code={
\tikzset{spiro2/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spiro2/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spiro2/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
 plot[variable=\t,domain=\pv{xmin}-0.002:\pv{xmax}+0.002,
    samples=\pv{samples},smooth] 
    ({(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
     {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})});
    }},
spiro2/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1,
dx/.initial=0.08,samples/.initial=21,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spiro2/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spiro2/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
\begin{document}
\begin{tikzpicture}
 \path (0,0)  
  pic[scale=0.5,draw=yellow,ultra   thick]{spiro2={dx=0.03}}
   foreach \X [count=\Y starting from 0] in {blue,red,purple,orange}
   {pic[scale=0.5,draw=\X,ultra
   thick]{spiro2={domain={-pi/12+\Y*pi/2}:{pi/12+\Y*pi/2}}}};
 % This is a loop orgy. We loop over scale factors, overall rotations and colors.   
 \path[line cap=round] (7,0)  
   foreach \ScaleN 
    [evaluate=\ScaleN as \Scale using {pow(0.85,\ScaleN)/0.8}] % compute sale factor
    in {1,...,5} %loop over scale
     {foreach \Z in {0,...,3} %loop over 4 overall rotations
       {foreach \X [count=\Y starting from 0] in 
         {yellow,orange,red,blue,purple,cyan,magenta,green!70!black} % colors
       {pic[scale=0.5,draw=\X,rotate=\Y*90/8+\Z*90,
       scale=\Scale,line width=\Scale*2pt]
       {spiro2={domain={-pi/11.4}:{pi/11.4}}}}}};
\end{tikzpicture}
\end{document}

修改 Spirograph 代码以获得更多控制

答案1

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